Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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The Maximal Covering Location Problem with Cost Restrictions

비용 제약 하에서 서비스 수준을 최대화화는 설비입지선정에 관한 연구

  • Hong, Sung Hak (Department of Computer Science and Industrial Systems Engineering, Yonsei University) ;
  • Lee, Young Hoon (Department of Computer Science and Industrial Systems Engineering, Yonsei University)
  • 홍성학 (연세대학교 컴퓨터과학.산업시스템공학과) ;
  • 이영훈 (연세대학교 컴퓨터과학.산업시스템공학과)
  • Published : 2004.06.30
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Abstract

This paper studied a maximal covering location problem with cost restrictions, to maximize level of service within predetermined cost. It is assumed that all demand have to be met. If the demand node is located within a given range, then its demand is assumed to be covered, but if it is not, then its demand is assumed to be uncovered. An uncovered demand is received a service but at an unsatisfactory level. The objective function is to maximize the sum of covered demand, Two heuristics based on the Lagrangean relaxation of allocation and decoupling are presented and tested. Upper bounds are found through a subgradient optimization and lower bounds are by a cutting algorithm suggested in this paper. The cutting algorithm enables the Lagrangean relaxation to be proceeded continually by allowing infeasible solution temporarily when the feasible solution is not easy to find through iterations. The performances are evaluated through computational experiments. It is shown that both heuristics are able to find the optimal solution in a relatively short computational time for the most instances, and that decoupling relaxation outperformed allocation relaxation.

Keywords

References

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